tensor_predictors/sim/sim_2e_ising.R

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2023-12-11 12:25:45 +00:00
library(tensorPredictors)
# library(logisticPCA)
# # library(RGCCA)
# # Use modified version of `RGCCA`
# # Reasons (on Ubuntu 22.04 LTS):
# # - compatible with `Rscript`
# # - about 4 times faster for small problems
# # Changes:
# # - Run in main thread, avoid `parallel::makeCluster` if `n_cores == 1`
# # (file "R/mgccak.R" lines 81:103)
# # - added `Encoding: UTF-8`
# # (file "DESCRIPTION")
# suppressWarnings({
# devtools::load_all("~/Work/tensorPredictors/References/Software/TGCCA-modified", export_all = FALSE)
# })
# setwd("~/Work/tensorPredictors/sim/")
# base.name <- format(Sys.time(), "sim_2e_ising-%Y%m%dT%H%M")
# # Source utility function used in most simulations (extracted for convenience)
# source("./sim_utils.R")
# # Set PRNG seed for reproducability
# # Note: `0x` is the HEX number prefix and the trailing `L` stands for "long"
# # which is `R`s way if indicating an integer.
# set.seed(seed <- 0x2eL, "Mersenne-Twister", "Inversion", "Rejection")
reps <- 100 # number of simulation replications
sample.sizes <- c(100, 200, 300, 500, 750) # sample sizes `n`
dimX <- c(5, 5, 5) # predictor `X` dimension
dimF <- c(2, 2, 2) # "function" `F(y)` of responce `y` dimension
betas <- Map(matrix, 1, dimX, dimF)
Omegas <- Map(function(p) `diag<-`(matrix(0.5, p, p), 0), dimX)
# data sampling routine
sample.data <- function(sample.size, betas, Omegas) {
dimX <- mapply(nrow, betas)
dimF <- mapply(ncol, betas)
# generate response (sample axis is last axis)
y <- runif(sample.size, -1, 1)
F <- aperm(array(c(
+sinpi(y), +sinpi(2 * y),
+cospi(y), +cospi(2 * y),
-cospi(y), -cospi(2 * y),
+sinpi(y), +sinpi(2 * y)
), dim = c(length(y), 2, 2, 2)), c(2, 3, 4, 1))
Omega <- Reduce(kronecker, rev(Omegas))
X <- apply(F, length(dim(F)), function(Fi) {
dim(Fi) <- dimF
params <- diag(as.vector(mlm(Fi, betas))) + Omega
tensorPredictors::ising_sample(1, params)
})
dim(X) <- c(dimX, sample.size)
list(X = X, F = F, y = y, sample.axis = 3)
}
sample.size <- 100L
# Sample training data
c(X, F, y, sample.axis) %<-% sample.data(sample.size, betas, Omegas)
# compute true (full) model parameters to compair estimates against
B.true <- Reduce(`%x%`, rev(betas))
# Build projections onto `all elements are equal except diagonal is zero` matrices
# proj.Omegas <- Map(function(Omega) {
# proj <- as.vector(Omega) %*% pinv(as.vector(Omega))
# function(Omega) {
# matrix(proj %*% as.vector(Omega), nrow = nrow(Omega))
# }
# }, Omegas)
proj.Omegas <- Map(.projMaskedMean, Map(as.logical, Omegas))
# data sampling routine
sample.data <- function(sample.size, betas, Omegas) {
dimX <- mapply(nrow, betas)
dimF <- mapply(ncol, betas)
# generate response (sample axis is last axis)
y <- runif(sample.size, -1, 1)
F <- aperm(array(c(
sinpi(y), -cospi(y),
cospi(y), sinpi(y)
), dim = c(length(y), 2, 2)), c(2, 3, 1))
Omega <- Reduce(kronecker, rev(Omegas))
X <- apply(F, 3, function(Fi) {
dim(Fi) <- dimF
params <- diag(as.vector(mlm(Fi, betas))) + Omega
tensorPredictors::ising_sample(1, params)
})
dim(X) <- c(dimX, sample.size)
list(X = X, F = F, y = y, sample.axis = 3)
}
# # has been run once with initial seed
# lpca.hyper.param <- local({
# c(X, F, y, sample.axis) %<-% sample.data(1e3, betas, Omegas)
# vecX <- mat(X, sample.axis)
# CV <- cv.lpca(vecX, ks = prod(dimF), ms = seq(1, 30, by = 1))
# # plot(CV)
# as.numeric(colnames(CV))[which.min(CV)]
# })
# set.seed(seed, "Mersenne-Twister", "Inversion", "Rejection")
lpca.hyper.param <- 10
# Create a CSV logger to write simulation results to
log.file <- paste(base.name, "csv", sep = ".")
logger <- CSV.logger(
file.name = log.file,
header = c("sample.size", "rep", outer(
c("time", "dist.subspace", "dist.projection"), # < measures, v methods
c("gmlm", "tnormal", "pca", "hopca", "lpca", "clpca", "tsir", "mgcca"),
paste, sep = "."
))
)
### for each sample size
for (sample.size in sample.sizes) {
# repeate every simulation
for (rep in seq_len(reps)) {
# Sample training data
c(X, F, y, sample.axis) %<-% sample.data(sample.size, betas, Omegas)
# start timing for reporting
start.timer()
# fit different models
# Wrapped in try-catch clock to ensure the simulation continues,
# if an error occures continue with nest resplication and log an error message
try.catch.block <- tryCatch({
time.gmlm <- system.time(
fit.gmlm <- gmlm_ising(X, F, y, sample.axis = sample.axis,
proj.Omegas = proj.Omegas)
)["user.self"]
time.tnormal <- -1 # part of Ising gmlm (not relevent here)
time.pca <- system.time(
fit.pca <- prcomp(mat(X, sample.axis), rank. = prod(dimF))
)["user.self"]
time.hopca <- system.time(
fit.hopca <- HOPCA(X, npc = dimF, sample.axis = sample.axis)
)["user.self"]
time.lpca <- system.time(
fit.lpca <- logisticPCA(mat(X, sample.axis), k = prod(dimF),
m = lpca.hyper.param)
)["user.self"]
time.clpca <- system.time(
fit.clpca <- convexLogisticPCA(mat(X, sample.axis), k = prod(dimF),
m = lpca.hyper.param)
)["user.self"]
time.tsir <- system.time(
fit.tsir <- TSIR(X, y, d = dimF, sample.axis = sample.axis)
)["user.self"]
# `mgcca` expects the first axis to be the sample axis
X1 <- aperm(X, c(sample.axis, seq_along(dim(X))[-sample.axis]))
F1 <- cbind(sinpi(y), cospi(y))
time.mgcca <- system.time(
fit.mgcca <- mgcca(list(X1, F1), ncomp = c(prod(dimF), 1L),
quiet = TRUE, scheme = "factorial")
)["user.self"]
}, error = print)
# Get elapsed time from last timer start and the accumulated total time
# (_not_ a precide timing, only to get an idea)
c(elapsed, total.time) %<-% end.timer()
# Drop comparison in case any error (in any fitting routine)
if (inherits(try.catch.block, "error")) { next }
# Compute true reduction matrix
B.gmlm <- with(fit.gmlm, Reduce(`%x%`, rev(betas)))
B.tnormal <- with(attr(fit.gmlm, "tensor_normal"), Reduce(`%x%`, rev(betas)))
B.pca <- fit.pca$rotation
B.hopca <- Reduce(`%x%`, rev(fit.hopca))
B.lpca <- fit.lpca$U
B.clpca <- fit.clpca$U
B.tsir <- Reduce(`%x%`, rev(fit.tsir))
B.mgcca <- fit.mgcca$astar[[1]]
# Subspace Distances: Normalized `|| P_A - P_B ||_F` where
# `P_A = A (A' A)^-1 A'` and the normalization means that with
# respect to the dimensions of `A, B` the subspace distance is in the
# range `[0, 1]`.
dist.subspace.gmlm <- dist.subspace(B.true, B.gmlm, normalize = TRUE)
dist.subspace.tnormal <- dist.subspace(B.true, B.tnormal, normalize = TRUE)
dist.subspace.pca <- dist.subspace(B.true, B.pca, normalize = TRUE)
dist.subspace.hopca <- dist.subspace(B.true, B.hopca, normalize = TRUE)
dist.subspace.lpca <- dist.subspace(B.true, B.lpca, normalize = TRUE)
dist.subspace.clpca <- dist.subspace(B.true, B.clpca, normalize = TRUE)
dist.subspace.tsir <- dist.subspace(B.true, B.tsir, normalize = TRUE)
dist.subspace.mgcca <- dist.subspace(B.true, B.mgcca, normalize = TRUE)
# Projection Distances: Spectral norm (2-norm) `|| P_A - P_B ||_2`.
dist.projection.gmlm <- dist.projection(B.true, B.gmlm)
dist.projection.tnormal <- dist.projection(B.true, B.tnormal)
dist.projection.pca <- dist.projection(B.true, B.pca)
dist.projection.hopca <- dist.projection(B.true, B.hopca)
dist.projection.lpca <- dist.projection(B.true, B.lpca)
dist.projection.clpca <- dist.projection(B.true, B.clpca)
dist.projection.tsir <- dist.projection(B.true, B.tsir)
dist.projection.mgcca <- dist.projection(B.true, B.mgcca)
# Call CSV logger writing results to file
logger()
# print progress
cat(sprintf("sample size (%d): %d/%d - rep: %d/%d - elapsed: %.1f [s], total: %.0f [s]\n",
sample.size, which(sample.size == sample.sizes),
length(sample.sizes), rep, reps, elapsed, total.time))
}
}
### read simulation results generate plots
if (!interactive()) { pdf(file = paste(base.name, "pdf", sep = ".")) }
sim <- read.csv(log.file)
plot.sim(sim, "dist.subspace", main = "Subspace Distance",
xlab = "Sample Size", ylab = "Distance")
# plot.sim(sim, "dist.projection", main = "Projection Distance",
# xlab = "Sample Size", ylab = "Distance")
plot.sim(sim, "time", main = "Runtime",
xlab = "Sample Size", ylab = "Time [s]",
ylim = c(0, max(sim[startsWith(names(sim), "time")])))